Jaime turns up in Darry, now ruled by Kevan Lannister's son Lancel, who was injured badly in the Battle of the Blackwater. We learn that Jaime has sent Wylis Manderley to Maidenpool to return him to his dad Wyman for killing Davos, who I still think is probably not dead.
Lancel is nowhere to be seen and Jaime is entertained by Lancel's wife Amerei and her mother Mariya. Her father is none other than Merrett Frey who was hanged by the Yellowcloak guy and the reanimated Catelyn in the epilogue of the last book. They try to get Jaime to go after Beric's outlaws and The Hound who apparently destroyed Saltpans, but Jaime isn't having it. (They know it is the Hound because of his distinctive helmet. Now that sounds like as blatant a red herring as there ever was, and we know it's not very in character behaviour for the Hound to be raping and pillaging whole towns.) Jaime says it should be up to Lancel to defend the lands.
But Lancel is too busy hanging out in the chapel being pious and feeling guilty about killing Robert and spilling his seed on Cersei. Jaime finds out he confessed this to the High Septon, which explains why the High Septon is now dead. He also finds out that Lancel is planning to give up his Lordship and go and fight for the new High Septon, because Cersei has agreed to allow the new High Septon to take up arms. Jaime thinks it's odd that she would allow this, but does not seem unduly alarmed. But he also seems vague about his history.
Darry is where they were all staying on the way to King's Landing back in the first book, when Arya got in a fight with Joffrey. In a weird interlude, Jaime confesses to the mute Ilyn Paine that he has had relations with his sister and planned to kill Arya. It's odd how likeable Jaime is in these chapters considering his aggression towards Stark children...